Spin transport studies in graphene

Our systematic analysis shows that,unlike monolayer graphene where the spin relaxation is due to a direct consequence of momentum scattering, in bilayer graphene the spin dephasing occur

SPIN TRANSPORT STUDIES IN GRAPHENE

JAYAKUMAR BALAKRISHNAN

DEPARTMENT OF PHYSICS NATIONAL UNIVERSITY OF SINGAPORE

SPIN TRANSPORT STUDIES IN GRAPHENE

DECLARATION

I hereby declare that the thesis is my original work and it has been written by me in its entirety I have duly acknowledged all the sources of information which have been used in the thesis

This thesis has also not been submitted for any degree in any university previously

-

Jayakumar Balakrishnan

ACKNOWLEDGEMENTS

I would like to thank Prof Barbaros Özyilmaz, my supervisor, for his patient guidance and constant support throughout the duration of my research Working in his group is a wonderful experience that will keep me motivated for the years to come I would like to sincerely thank all my ‘Gurus’, whose blessings have helped me to reach this memorable phase in life

I am also grateful to Dr Zheng Yi, Dr Xu Xiangfan and Dr Manu Jaiswal for their support and guidance during the early years of chaos and confusion More importantly, I owe them my gratitude for making me understand the importance of the minute details and tricks while performing low temperature transport measurements I am also grateful to Prof A H Castro Neto, Prof M A Cazalilla and

Dr Aires Ferreira for the stimulating discussions and theoretical help

My sincere thanks to Mr Gavin Kok Wai Koon, Mr Ahmet Avsar and Mr Yuda Ho; whose constant support has made this work possible and helped me to achieve the goals set for my Ph.D I would also like to thank Prof Gernot Güntherodt, Prof Bernd Beschoten, Dr Mihaita Popinciuc, Mr Frank Volmer and

Mr Tsung-Yeh Yang from the RWTH AACHEN University for their help in the fabrication and characterization of spin-valve devices during the initial stages of my work

I also thank my colleagues Dr Ni GuangXin, Dr Zeng Minggang, Dr Xie Lanfei, Dr Surajit Saha, Dr Ajit Patra, Ms Zhang Kaiwen, Mr Zhao Xiangming, Mr Orhan Kahya, Mr Alexandre Pachoud, Mr Toh Chee Tat, Mr Henrik Anderson, Mr

Wu Jing, Mr Jun Yu, Dr Ajay Soni, Mr Ibrahim Nor, Mr Zhang Shujie, Mr Ang Han Siong, Dr Raghu, Dr J H Lee and all other members of the lab, who were all there at each phase and have constantly helped me during my research works I would like to

have a special mention of late Mr Tan, our workshop manager, who was always there to

help us with a gentle smile

I would also like to thank my friends Ram Sevak, Vinayak, Suresh, Pranjal, KMG, Sumit, Ashwini, Manoj, Vaibhav, Amar and all others who have made my stay in Singapore a memorable one Finally, I would like to thank my parents, my sister and my brother-in-law, who have always backed me with my decisions and encouraged me to follow my dreams, without which I would never have reached this point in life

Table of Contents

1.1 Spintronics: an overview 2

1.2 Thesis Outline 5

Bibliography 8 2 Basic Concepts and Theory 11 2.1 Introduction 11

2.2 Spin transport: Basic theory 12

2.2.1 Spin diffusion without drift 14

2.3 Spin injection and detection via non-local spin valves 15

2.3.1 Electrical spin injection into a non-magnetic material 16

2.3.2 Detection of the decaying spins 17

2.3.2.1 Detection of spins by spin-valve effect: 18

2.3.3 Four terminal non-local spin-valve geometry 19

2.3.4 Conductivity mismatch and tunnel barriers 21

2.3.4.1 F/I/N/I/F spin-valve 22

2.4 Electron spin precession in an external magnetic field 26

2.4.1 Spin precession in ballistic transport regime 27

2.4.2 Spin precession in diffusive transport regime 28

2.5 Spin relaxation mechanisms 30

2.5.1 Elliott-Yafet spin scattering 30

2.5.2 D’yakonov-Perel spin scattering 31

2.5.3 Bir-Aronov-Pikus spin scattering 32

2.5.4 Spin scattering due to hyperfine interaction 33

2.6 Spin-orbit coupling 33

2.6.1 Spin-orbit coupling: atomic picture 33

2.6.1.1 Dependence of SOC strength on the atomic number 35 2.6.2 Spin-orbit coupling in solids 36

2.6.3 Spin dependent scattering due to spin-orbit coupling 37

2.6.3.1 Intrinsic spin-orbit coupling: Dresselhaus and Rashba spin-orbit interaction 37

2.6.3.2 Extrinsic spin-orbit coupling 38

2.6.3.3 Skew scattering 38

2.6.3.4 Side-jump 39

2.7 Spin Hall Effect 42

2.7.1 Generation and detection of spin currents via SHE 43

2.7.2 Electrical detection of spin currents 43

2.7.3 Non-local spin detection in the diffusive regime using H-bar geometry 46

2.7.4 Magnetic field dependence of the non-local signal 47

2.8 Graphene 49

2.8.1 Electronic properties of graphene 50

2.8.1.1 Band structure of graphene 51

2.8.2 Electronic properties of bilayer graphene 56

2.8.2.1 Band structure of bilayer graphene 57

2.8.2.2 Semiconductors and bilayer graphene: A comparison 58 2.8.3 Graphene spintronics 59

2.8.3.1 Spin relaxation in graphene 60

Bibliography 62 3 Experimental Techniques 68 3.1 Introduction 68

3.2 Graphene: sample preparation 68

3.2.1 Mechanical Exfoliation 69

3.2.2 Large area growth of graphene by chemical methods 71

3.3 Graphene: sample characterization 73

3.3.1 Raman characterization 73

3.3.1.1 Determining the number of graphene layers 74

3.3.1.2 Determining the quality of graphene: Effect of disorder 75 3.3.2 Atomic Force Microscopy 76

3.4 Tunnel barrier: Growth and characterization 77

3.4.1 Optimization of tunnel barrier growth 79

3.5 Device Fabrication 80

3.5.1 Spin-valves 80

3.5.2 Spin Hall devices 83

3.6 Device Characterization 85

3.6.1 Spin transport measurements 86

Bibliography 88 4 Spin Transport Studies in Mono- and Bi-layer Graphene Spin-valves1 90 4.1 Introduction 90

4.2 Characterization of mono- and bi- layer graphene spin-valves 91

4.2.1 Spin injection and spin transport in bilayer graphene 93

4.2.1.1 Non-local spin valve measurements: 93

4.2.1.2 Hanle spin-precession measurements: 95

4.2.2 Identifying the spin scattering/dephasing mechanism in bilayer graphene 96

4.2.2.1 Spin relaxation time τ s vs charge carrier mobility µ: 97 4.2.2.2 Spin relaxation time τ s vs conductivity σ: 98

4.2.2.3 Spin relaxation time τ s vs.charge carrier density n 100 4.2.2.4 Effect of electron-hole puddles at the charge neutrality point 102

4.2.3 Estimate of the spin-orbit coupling strength in bilayer graphene 103 4.2.3.1 From conductivity data 104

4.2.3.2 From Mobility data 104

4.3 Conclusion 106

Bibliography 107 5 Colossal Enhancement of Spin-Orbit Coupling in Weakly Hydro-genated Graphene1 110 5.1 Introduction 110

5.2 Functionalization of Graphene 111

5.2.1 Hydrogenation of graphene 112

5.3 Characterization of the hydrogenated graphene samples 113

5.3.1 Raman Characterization 113

5.3.2 Charge transport characterization 115

5.3.2.1 Is the transport in our devices in the diffusive regime or in the ballistic regime? 117

5.3.3 Determination of percentage of hydrogenation 118

5.3.3.1 Estimate from Raman Data 118

5.3.3.2 Estimate from Transport data 119

5.4 Spin transport studies in weakly hydrogenated graphene devices 120

5.4.0.3 Eliminating contributions from spurious thermoelec-tric effects to the measured non-local signal 122

5.4.1 Carrier density dependence of the non-local signal 123

5.4.2 Spin precession measurements in an external in-plane magnetic field 123

5.4.2.1 Important note on precession measurements: 125

5.4.2.2 Non-local signal as function of perpendicular magnetic field: 126

5.4.3 Length and width dependence of the Non-local signal 128

5.4.3.1 Length dependence 128

5.4.3.2 Width dependence 128

5.5 Spin - orbit coupling in weakly hydrogenated graphene devices 131

5.5.1 Estimation of τ p and τ s 131

5.5.2 Determination of SO coupling strength 132

5.5.3 Comparison with lateral spin valve data for hydrogenated Graphene135 5.5.4 Identification of the spin scattering mechanism 136

5.6 Conclusion 136

Bibliography 138 6 Giant Spin Hall Effect in CVD Graphene1 141 6.1 Introduction 141

6.2 Cu-CVD graphene 143

6.3 Characterization graphene samples 143

6.3.1 Nature of Cu adsorption on Graphene 144

6.4 Transport measurements 147

6.4.1 Charge transport measurements 147

6.4.2 Non-local measurements 148

6.4.2.1 Spin-valve measurements 148

6.4.2.2 Spin Hall measurements 149

6.4.3 Length and width dependence of the non-local signal 151

6.4.4 In-plane magnetic field dependence of the non-local signal 153

6.5 Identifying the cause for giant spin Hall effect in CVD graphene 154

6.6 Control experiments on exfoliated graphene with metallic adatoms 157

6.6.1 Sample preparation 157

6.6.1.1 Introduction of Cu adatoms 157

6.6.1.2 Au and Ag deposition 158

6.6.2 Transport measurements 159

6.6.2.1 Additional note on in-plane magnetic field dependence 161 6.7 Estimate of spin-orbit coupling strength 161

6.8 Identifying dominant spin Hall scattering mechanisms 164

6.8.1 Theoretical modelling for giant γ 166

6.8.1.1 Choice of parameter 171

6.8.1.2 Driving mechanisms for the spin Hall effect 172

6.9 Conclusion 172

Bibliography 174 7 Summary and Outlook 178 7.1 Spin-valve experiments 178

7.2 Spin Hall experiments 180

The work described in this thesis is an attempt to understand the spin transportproperties of graphene - the weakly spin-orbit coupled two dimensional allotrope ofcarbon In the first half of the thesis we make an effort to understand the spin re-laxation mechanisms in monolayer and bilayer graphene For this, four-terminal spinvalve devices are characterized in the non-local geometry and a correlation betweenthe charge and spin parameters has been drawn Our systematic analysis shows that,unlike monolayer graphene where the spin relaxation is due to a direct consequence

of momentum scattering, in bilayer graphene the spin dephasing occurs due to theprecession of spins under the influence of local spin-orbit fields between momentumscattering The role of intrinsic and extrinsic factors that could lead to such contrast-ing results is discussed

The second half of the thesis focuses on enhancing the spin-orbit interaction ingraphene by introducing adatoms Our pioneering experiments in graphene sam-ples decorated with adatoms, demonstrate a three orders of magnitude increase inspin-orbit interaction strength while preserving the unique transport properties ofintrinsic graphene In such samples, we realize for the first time room-temperaturenon-local spin Hall effect at zero applied magnetic fields Moreover, the methods em-ployed for the introduction of adatoms, specifically the metallic adatoms, in graphenecan easily be generalized for any metal, and would thus allow for the future realization

of a graphene-based two dimensional topological insulator state

List of Figures

2.1 Decay of the spin density s as a function of the position x Here at x

= 0 the spin density is normalized to 1 and as the distance increases

from x = 0 the spins start to decay with a characteristic length scale λ s 142.2 Measurement schematics for (a) a two terminal spin-valve device and(b) a four terminal non-local spin-valve device The current and voltageprobes are marked in the schematics 192.3 A typical non-local signal measured for a graphene based spin-valve 202.4 Schematics of F/I/N/I/F non-local spin-valve structure The top leftinset shows the resistor model for F/I/N spin injector and the top rightinset shows the resistor model for the voltage probe 242.5 Schematics of the spin precession measurement in non-local geometrywhen both the injector and detector ferromagnets have (a) parallelmagnetization and (b) anti-parallel magnetization with the externalmagnetic field applied perpendicular to the initial direction of the spin 262.6 Modulation of the spin signal in an external magnetic field due to spinprecession in the ballistic transport regime The red and blue curverepresents the spin signal modulation for the relative parallel and anti-parallel magnetization between the injector and detector electrodes 272.7 Modulation of the spin signal in an external magnetic field due to spinprecession in the diffusive transport regime for graphene spin-valves.The red curve represents the fit to the data points 29

2.8 Schematics for Elliott-Yafet spin scattering Here, the momentum tering by impurities or phonons has a finite probability to flip the elec-tron spin 302.9 Schematics for D’yakonov-Perel spin scattering Here, the electron spinprecess about the momentum dependent magnetic field 312.10 Schematics for Bir-Aronov-Pikus spin scattering.Here, the electron ex-changes spin with holes of opposite spin, which then undergoes spinrelaxation via Elliott-Yafet scattering 322.11 The trajectory for the spin-up and spin-down electrons after skew scat-

scat-tering The angle δ represents the angle at which the electrons get

deflected 382.12 The trajectory for the spin-up and spin-down electrons after side-jump

scattering The vector ⃗ δ represents the opposite sideways displacement

of the electrons with up and down spins 402.13 The trajectory for the spin-up and spin-down electrons due to spinHall effect The longitudinal charge current induces transverse spinaccumulation 422.14 Schematics showing the measurement configuration for the detection

of the spin accumulation by non-local inverse spin Hall effect Herethe spin is injected into the normal metal using a ferromagnet withmagnetization M 442.15 Schematics showing the measurement configuration for the injectionand detection of the spin accumulation by non-local H-bar geometry.Here the spin separation is generated in the normal metal by spin Halleffect while the detection is realized by the inverse spin Hall effect 452.16 In-plane magnetic field dependence of the non-local spin Hall signal.The damped oscillatory behaviour of the non-local signal is a clearsignature for the spin precession in the medium 48

2.17 Lattice structure of graphene with two interpenetrating triangular tices 502.18 Energy-momentum dispersion relation for graphene 542.19 (a) Gate voltage tuning of the graphene’s Fermi energy and (b) the

lat-same graph shown as a function of the charge carrier density n The

charge carrier density is calculated using equation (2.8.24) 572.20 The band structure of graphene (a) without bias field i.e V = 0 and(b) with bias field V̸= 0 Here γ ⊥ = 0.4 eV 58

3.1 Optical image: (a-f) Various steps involved in the mechanical foliation of graphene using the ’scotch tape’ method and (g) showsthe different optical contrast for a single layer mechanically exfoliatedgraphene (SLG) adjacent to a multilayer graphene flake (MLG) on a

ex-300 nm SiO2 substrate 703.2 Optical image of CVD graphene grown after transferring onto a 300

nm SiO2 substrate The inset shows the magnified picture of the CVDgraphene samples In general, there are islands of bilayer grapheneflowers in between the single layer graphene region 723.3 Raman mapping for the (a) 2D band and (b) G band for a SLG Hallbar device (c & d) The Raman spectrum for a SLG and BLG showing

G and 2D bands with a characteristic 2D band FWHM∼ 23 cm −1 and

56 cm−1 respectively 743.4 Evolution of the D-peak intensity at wavenumber 1350 cm−1 with in-creasing defect density Here the defects are introduced by progres-sively hydrogenating the HSQ coated graphene samples by e-beam ir-radiation The e-beam dose range from 0-8 mC/cm2 763.5 Atomic force microscopy (AFM) image of an (a) exfoliated graphenesample on a SiO2 substrate (b) CVD graphene sample on a SiO2substrate showing the presence of CVD growth specific ripples andwrinkles 77

3.6 Atomic force microscopy (AFM) image of MGO-deposited graphenesample on a SiO2 substrate The image clearly shows that (a) withoutannealing or (b) with annealing only at 100◦ after MgO depositionresults in a non-uniform growth of the tunnel barrier 783.7 Atomic force microscopy (AFM) images showing the sequences andoptimal conditions for the deposition of a uniform MGO layer on agraphene sample on a SiO2 substrate 793.8 Optical images showing (a) the alignment markers adjacent to graphenesamples (b & c) the Design CAD file with electrode patterns designedfor the specific sample shown in (a) and (d) the final device structure

on graphene after e-beam lithography and development 813.9 Scanning electron microscopy (SEM) image of a graphene spin-valvedevice after liftoff showing multiple junctions The electrodes high-lighted in blue represent one spin valve junction 823.10 The optical images of graphene showing (a) the device after lift-off andprior to etch mask writing (b) the device after writing etch mask todefine the Hall bar geometry and (c) the final Hall bar device after O2plasma etching of the etch channel 843.11 Schematics showing the measurement set-up for transport measurement 863.12 The sample holder in the rotating probe The sample holder can be ro-tated to align the sample parallel to- or perpendicular to- the direction

of the applied magnetic field 874.1 (a) Atomic force microscopy image of a bilayer graphene sample afterMgO deposition: rms roughness∼ 0.3 nm (b) Scanning electron mi-

croscope image of a bilayer graphene sample with multiple non-localspin valves 91

4.2 (a) Carrier density dependence of BLG resistivity for the temperature

range 2.3-300 K (b) The momentum relaxation time, τ p = σm ∗/ne2

calculated in the Boltzmann framework as a function of carrier density

n for BLG at T = 300 K (black circles), 50 K (red circles), and 5 K

(blue circles) 924.3 (a-c) Schematics of non-local spin valve showing the non-local mea-surement procedure in an in-plane magnetic field Measurements areperformed with standard a.c lock-in techniques at low frequencies

with currents in the range of 1-10 µA (d) Non-local resistance for a

bilayer graphene sample as a function of the in-plane magnetic field.The blue and red arrows show the field sweep direction while the blackarrows show the relative magnetization orientations of the injector anddetector electrodes 944.4 Hanle precession measurement for a perpendicular magnetic field Bz(T)

sweep for (a) the same sample in figure 4.3(b) with µ ∼ 2000cm2/Vs

and (b) for a sample with µ ∼ 300cm2/Vs 954.5 Results of Hanle precession measurements for BLG samples with mo-bility varying from 200-8000 cm2/Vs τ s vs µ plotted on a log-log scale

(a) at room temperature and (b) at low temperature, 5 K 974.6 τ s vs σ min for bilayer graphene samples of figure 4.5 at room temper-ature 99

4.7 (a) Upper panel: Resistance vs n for single layer graphene at 5 K and

at 300 K; Lower panel: τ s vs n for T = 300 K (black circles) and 5 K (red circles), (b) Upper panel: Resistance vs n for bi layer graphene

at 5 K, 50 K and at 300 K; Lower panel: τ s vs.n for T = 300 K (black

circles), 50 K (blue circles), and 5 K (red circles) and (c) Upper panel:

τ s vs T for four densities n = CNP (black circles), 0.7 × 1012/cm2(red circles), 1.5 × 1012/cm2 (blue circles) and 2.2× 1012/cm2 (green

circles) for bilayer graphene; Lower panel: τ s vs T for two densities

n = CNP (black circles), 1.5 × 1012/cm2 (blue circles) for single layergraphene 1004.8 (a) The momentum relaxation time, τ p = σm ∗/ne2 calculated in the

Boltzmann framework as a function of carrier density n for BLG at

T = 300 K (black circles), 50 K (red circles) and 5 K (blue circles);

(b, c and d) The carrier density dependence of the product τ s τ p and

the ratio τ s /τ p, which identifies the dominant scattering mechanism

for T = 300 K, 50 K and 5 K, respectively A constant value for τ s τ p

indicates DP while a constant value for τ s /τ p indicates EY mechanism

The arrow in figure b shows the significant change in the ratio τ s /τ p with density at RT when compared to the change inτ s τ p 1024.9 στ s vs n for a bilayer graphene device From the slope, the Larmor

frequency for spins can be estimated 1055.1 Schematics showing the lattice deformation due to the functionaliza-tion of graphene with adatoms like hydrogen 111

5.2 (a) The Raman spectrum of graphene coated with HSQ after tion with e-beam (dose 0-8 mC/cm2) The progressive increase in theD-peak intensity results from the hydrogenation of the graphene sam-ple (b) The evolution of the Si-H peak at 2265 cm−1 as a function ofe-beam dose With increasing dose the peak intensity decreases drasti-cally indicating the dissociation of the hydrogen from the HSQ (c) TheRaman spectrum for a single graphene device showing the reversibil-ity of hydrogenation upon annealing in Ar environment at 250◦C for

irradia-2 hours A constant Ar gas flow of 0.3L/min is maintained out the annealing process The near vanishing of the D-peak afterannealing confirms that HSQ e-beam irradiation introduces minimumvacancies in the graphene system 1145.3 (a) Scanning electron micrograph of a hydrogenated graphene sample

through-showing multiple Hall bar junctions Scale bar, 5 µm (b) ρ vs n for

pristine and hydrogenated graphene 1155.4 Resistance as a function of temperature at CNP (red solid circles) and

at n =1×1012/cm2(blue solid circles) (a) for pristine graphene and (b)for weakly hydrogenated graphene Note that the data presented in(a) and (b) are for two distinct samples (c) low temperature R vs Tfor weakly hydrogenated graphene fitted for logarithmic corrections of

the form ρ = ρ0 + ρ1ln(T0/T); where ρ0 = 10251 Ω, and ρ1 = 166 Ω 1165.5 (a) The evolution of the integrated ID/IGratio of graphene coated withHSQ samples irradiated with increasing e-beam dose (b) The evolution

of the percentage of hydrogenation with increasing irradiation dose forHSQ (0- 5mC/cm2) calculated from the ID/IG ratio 1185.6 The σ vs n plot for one of the G/HSQ samples irradiated with an e-

beam dose of 1mC/cm2 The red curve is the fit to the conductivityfor resonant scatterers which gives an impurity density nimp = 1 ×

1012/cm2 119

5.7 (a) Measurement schematics for the non-local spin Hall measurement.Inset: schematics showing the deformation of the graphene hexagonallattice due to hydrogenation (b) RN L versus n for pristine graphene(blue) and hydrogenated graphene 0.02% (red) at room temperature.The dark grey dashed lines show the ohmic contribution to the mea-sured signal for pristine graphene (c) Dependence of the RN L on thepercentage of hydrogenation The dark grey dashed lines show thecalculated ROhmic contribution for this sample 1205.8 The I-V characteristics of the non-local signal The linear dependence

of the I-V curve clearly excludes the possibility of any dominant moelectric contribution to the non-local signal 1225.9 Parallel-field precession data for the sample with L/W∼ 5 and mobility

ther-∼ 20,000 cm2 /Vs (a) raw data and (b) same data after a backgroundhas been subtracted from the raw data The red dotted line is the fit

for the experimental curves The fitting gives λ s ∼ 1.6 µm (c-d) for a

second sample with λ s ∼ 2.8 µm 124

5.10 The non-local signal, RN L vs n The black dashed lines show thecalculated leakage current contribution and (b) the precession mea-surement for the same sample 1255.11 RN L vs n for different perpendicular magnetic fields in the range 0- 4

T for (a) sample with L (2 µm)/W (1 µm) = 2 and (b) sample with L (2 µm)/W (0.4 µm) = 5 1265.12 The absence of any anomalous Hall signal at zero magnetic field forthe weakly hydrogenated sample at T = 3.4 K 127

5.13 Length dependence of RN L at room temperature (a) At the CNP and(b) at n = 1×1012 cm−2 (b) for samples with 0.02%(red solid circles)and 0.05% (blue solid circles) hydrogenation Here the length is thecenter-center distance between the injector and detector electrodes.The solid lines are the fit for the data and the dark grey dashed line isthe calculated ohmic contribution at these charge carrier densities 1295.14 RN L (red circles) as a function of width W (W= 400 nm -1.8 µm) for

a fixed length L (2 µm) The solid red line is the fit for the data and

the dark grey dashed line is the calculated ohmic contribution (inset:

R versus W on a linear scale) 130

5.15 τ s vs τ p for weakly hydrogenated graphene devices 1325.16 (a) The non-local spin-valve resistance as a function of the in-planemagnetic field.The horizontal arrows show the field sweep directionand (b) the Hanle precession measurement for perpendicular magneticfield for the same junction The fitting gives a spin relaxation time of

200 ps which is in good agreement with the values extracted from thespin Hall measurements 1356.1 (a) AFM data for graphene sample decorated with Cu nanoparticles.The Particle Analysis function gives the details of the distribution ofthe particle sizes on graphene and the average Cu nanoparticle size forthis sample is about 32 nm 144

6.2 (a) Raman mapping of a Cu-CVD graphene spin Hall device showing2D, G and D bands The high quality of the CVD graphene can beinferred from the weak D-band intensities The D-peak intensities aremore prominent along the edges of the device which is due to the oxy-gen plasma induced defects at the edges, (b) Energy dispersive X-rayspectroscopy (EDS) using TEM The samples for TEM measurementsare prepared on a standard TEM gold grids The size of each grid is

7 µm X 7 µm The additional Au peaks in the EDS spectrum is due

to the presence of Au TEM grids on which the graphene samples areprepared and (c) XPS data for CVD graphene showing the C1s peakand the inset shows the measured Cu 2p peaks 1456.3 (a & b) Comparison of Raman 2D and G peak positions for Cu-CVDand exfoliated graphene samples and (c) Raman G-peak shift for hy-drogenated graphene sample showing the chemisorbed nature of theadsorption 1466.4 (a) Optical image of 3×3 array of devices on Si/SiO2substrate togetherwith the SEM image of the active area of a typical spin Hall device (b)AFM 3D surface topography of a typical CVD spin Hall device withdetails of actual measurement configurations and (c) the longitudinalresistivity as a function of carrier density for opposite pair of contacts(blue and red curves) Inset: Transverse resistance as a function ofgate voltage showing the absence of any zero field Hall signal, thuseliminating the possibility of magnetic moments due to adatoms 1476.5 Non-local spin-valve measurements: (a) RNL vs B|| and (b) Hanleprecession measurements for Cu-CVD graphene samples 148

6.6 (a) Schematics showing the non-local measurement geometry and local signal RN L vs charge carrier density for pristine graphene sam-ples and Cu-CVD graphene samples The dotted lines represent thecalculated Ohmic leakage contribution The L/W ratios for all thesamples are ∼ 2 150

(b)non-6.7 Length and width dependence of the non-local signal for Cu-CVDgraphene The inset shows the RN L vs n for different L/W ratio 1516.8 In-plane magnetic field dependence of the non-local signal for two Cu-CVD graphene samples The amplitude of the oscillatory signal dimin-shes as we move away from the charge neutrality point Inset: In-planefield dependence for a pristine exfoliated sample 1536.9 (a) Length dependence of the non-local signal for exfoliated graphenesamples dipped in the etchant solution, ammonium per sulfate Themeasured non-local signal is comparable to the calculated Ohmic con-tribution (Inset: RNL vs n for one junction) (b) Length dependence

of the non-local signal for Cu-CVD graphene sample, before and ter vacuum annealing at 400K for 24 hours (c) Measured non-localvoltage as a function of the source-drain current (VN L vs ISD) 1556.10 (a) SEM data for graphene sample decorated with Au nanoparticlesand (b) AFM data on final spin Hall device with Au nanoparticles 1586.11 (a & b) Length and width dependence of the non-local signal for ex-foliated graphene decorated with Cu, Ag and Au adatoms The greydotted line shows the measured non-local signal (which is equal to theOhmic contribution) for a pristine graphene sample (Inset: RN L vs n)

is the ideal spin Hall angle as generated by SOC active dilute Cu ters in otherwise perfect graphene generated via SS The (solid) orange

clus-line shows the realistic γ taking into account other sources of disorder

(modelled here as resonant scatterers) Calculations performed at roomtemperature; other parameters as given in main text 1666.16 the Fermi energy dependence of the longitudinal (charge) conductivity

at room temperature for the Cu-CVD graphene sample The (solid)orange line shows the theoretical value of the conductivity as computedfrom Eq 6.8.5 The excellent qualitative agreement shows that fitparameters are consistent with charge transport characteristics of thesystem (Parameters as in Fig 6.15.) 1717.1 a) Resistance of the weakly hydrogenated graphene sample as a func-tion of the carrier density for different tilt angles Here the perpendicu-lar magnetic field is kept at a constant value while varying the in-planefield The graph is shifted in the y-axis for better visibility (b) thesame graph showing the change in the phase of the SdH peaks withvarying tilt angle.(c) R*n vs n of the weakly hydrogenated graphenesample for different tilt angles the graph shifted in the y-axis for bettervisibility 181

List of Tables

6.1 Fitting parameters from L and W dependence 1526.2 Adatom distribution 1596.3 Spin parameter for graphene decorarted with metallic adatom 161

Chapter 1

Introduction

The development of quantum mechanics in the early half of the twentieth century hasenabled a deeper understanding of the fundamental particles that constitute matter.The electrons, the first understood elementary particle, with a negative elementaryelectric charge and half-integer intrinsic angular momentum (spin) plays an impor-tant role in the current technological developments Depending on the fundamentalproperty which is being manipulated, two closely related but independent fields haveemerged: (1) electronics, where the charge of electron is manipulated for logical oper-ations and transistor functionalities and (2) spintronics, where the electron’s intrinsicangular momentum, called spin, is manipulated The electron’s spin angular momen-tum (in units of ~) can have two values of 1/2 (spin-up) or -1/2 (spin-down) whenplaced in a magnetic field, allowing binary logical operations The aim of this chapter

is to give a short introduction on the developments in the emerging field of ics At the end of the chapter an outline of this thesis with short summaries on eachchapter is provided

spintron-1.1 Spintronics: an overview

Spintronics [1] refers to the study of the electrical, optical and magnetic properties

of materials, due to the presence of non-equilibrium spin populations In a broadersense, spintronics is the study of spin phenomena like spin-orbit, hyperfine and/orexchange interactions Such insights into spin interactions allow us to learn moreabout the fundamental processes leading to spin relaxation and/or spin dephasing inmetals, semiconductors and semiconductor heterostructures [2]

The first observations of the effects of electron spins on the charge transport can

be dated back to 1857 [3, 4], even before the discovery of electrons (J.J Thomson1897) The observation that the resistance of the ferromagnet relies on the relativeangle between the charge current direction and the magnetization direction in theferromagnet [3, 4], termed as the anisotropic magneto resistance (AMR), has sincebeen an important topic of study [5, 6] After the discovery of electrons in 1897and the development of quantum mechanics in the early half of the 20th century[7], the fundamental studies in understanding the puzzling observations in the linespectra of atoms led to the proposal of an intrinsic angular momentum for electrons

by Uhlenbeck and Goudsmit in 1925 [8, 9] This intrinsic angular momentum, known

as spin interacts with magnetic field and attains quantized values of 1/2 or -1/2 Sincethese quantized values of 1/2 or -1/2 can be used in a similar way to the Booleanlogical operations based on binary numbers 0 and 1, a new field where the spin degree

of freedom of electron is utilized for the realization of spin based electronic applicationshas emerged [1, 2, 10–12] The potential applications of spintronics range from spinfield effect transistors [13], magnetic random access memories [14], spin-based light

emitting diodes (LED’s) [15] to topological quantum computations [10] However, aneffective utilization of the spins for information processing requires three importantcriteria to be satisfied: (1) the injection of spin polarized current into the material ofinterest, metals, semiconductors etc., (2) an ideal material with a long spin relaxationlength in which the injected spins can diffuse, and (3) a detector for the spins [2].One of the first realistic proposals for the injection of spins came from Aronov andPikus in 1976 where they proposed the electrical spin injection as a method to createnon-equilibrium spin population in non-magnetic materials [16, 17] Experimentallythe electrical spin injection in metals was realized by Johnson and Silsbee in 1985 insingle crystal aluminum [18–20] However, until 1988 the field of spintronics remained

of interest for fundamental studies only In 1988-89 two groups led by Albert Fert inFrance and Peter Gr¨unberg in Germany( Nobel Prize in Physics 2007) discovered thegiant magnetoresistance in a ferromagnet/metal/ferromagnet heterostructure [21–25]

It was shown that the relative orientation of the magnetization in the ferromagneticlayers determined the electrical resistance of the heterostructure The change in theresistance between parallel and anti-parallel configurations of the magnetization inthe ferromagnetic layers could be greater than 100%; hence the name giant magnetoresistance (GMR) These discoveries were later followed by the demonstration ofGMR-based magnetic read heads in commercially available hard drives The GMR-based magnetic read head is one of the first and foremost applications of spintronicstill date

The discovery of the GMR also triggered the renewed interest for new spin-dependentelectron transport in metals as well as in semiconductor heterostructures Notable

among these phenomena were (1) the tunneling magneto resistance (TMR) in netic tunnel junctions [26–28], (2) the electrical injection of spins into a non-magneticmedium (metals and semi-conductors) employing a four terminal non-local lateralspin-valve geometry [29–32], and (3) the creation of non-equilibrium spin population

mag-in metals and semi-conductors by the spmag-in Hall and mag-inverse spmag-in Hall effects [33–36].Specifically, the spin transport in semiconductors attracted much attention due totheir unique properties such as the presence of a band gap which allows the injectionand detection of spins via optical means For instance, the experimental demonstra-tion of the spin Hall effect was first reported in GaAs semiconductor by spatiallyresolving the Kerr rotation of the reflected light from the samples [35] However, ademerit of the semiconductor and metal spintronics is the low spin relaxation length

of charge carriers due to the enhanced flip scattering induced by the high orbit coupling strength This calls for new materials where the spin-orbit couplingcan be manipulated with minimal compensation of the spin relaxation length

spin-An ideal source of materials which could allow such long spin relaxation length arethe organic conductors like carbon nanotubes [37] and graphene [6] Carbon being alight element (Z = 6), the intrinsic spin-orbit coupling (∝ Z4) is weak and hence thedominant spin dephasing mechanism due to spin-orbit coupling is also weak [39] This

allows fora spin relaxation length of the order of 100µm in these materials [40, 41].

Moreover, it is also easy to functionalize these carbon-based materials with reactiveelements like hydrogen and fluorine [42] and also by metallic adatoms [43] Suchcontrolled additions of adatoms are predicted to enhance the spin-orbit coupling ingraphene without affecting its long spin relaxation length In this thesis I will discussour recent results in understanding the spin transport properties of graphene and

functionalized graphene.

The main focus of this thesis is to understand and study the spin transport properties

in the newly discovered perfect 2D material ”Graphene” and its chemically/physicallyfunctionalized derivatives For this, we first utilize the non-local spin-valve geometrywith a Ferromagnet (Co)/Tunneling barrier (MgO)/Graphene/Tunnel barrier(MgO)/Ferromagnet (Co) structure The aim of these studies are to understand and con-trast the fundamental spin relaxation/scattering mechanisms in single- and bi-layergraphene As a next step we manipulate the electron spins in graphene via the spinHall effect Besides being of interest from a fundamental physics perspective, thistechnique will also allow the transport and detection of spins without the need forany magnetic elements This is of utmost importance for future applications since itallows manipulation of spins by the simple application of a voltage However, due tothe low spin-orbit coupling of carbon atoms, this effect is feasible only at ultra-lowtemperatures in graphene and necessitates new methods to enhance the spin-orbitcoupling in graphene

Among the different approaches proposed, the decoration of graphene with adatomsholds a lot of promise Here, the graphene spin-orbit coupling can be enhanced intwo different ways: (1) by chemical functionalization of graphene with adatoms likehydrogen and fluorine [44] and (2) by the introduction of metallic adatoms like copper(Cu) or gold (Au) which due to its proximity to the graphene lattice allows electrontunneling from graphene to the adatoms and back resulting in a local enhancement of

the spin-orbit coupling strength [43] Our aim in this work will be to see the predictedenhancement in spin-orbit coupling in graphene by the introduction of adatoms Forthis we take hydrogen, gold and copper as the model systems A brief outline for theindividual chapter in this thesis is given below:

Chapter 2: The basic concepts essential for understanding the spin transport in magnetic materials is introduced The chapter will focus on the theoretical back-ground required for understanding the non-local spin transport measurements in theconventional lateral spin-valve geometry This will be followed by an introduction tothe spin Hall and inverse spin Hall effects After discussing these basic spin transporttheory, a brief introduction to graphene and graphene spintronics is provided

non-Chapter 3: This chapter will focus on the basic experimental techniques required toperform the spin transport measurement in the spin-valve as well as in the spin Hallgeometry This includes graphene sample preparation, identification of single andbi-layer graphene, device fabrication and characterization

Chapter 4: The experimental results on the spin transport in graphene spin-valves arediscussed The main focus of this chapter will be to differentiate the spin transport

in single- and bi-layer graphene with emphasis given to identify the dominant spinscattering mechanism in bilayer graphene

Chapter 5: This chapter discusses the controlled functionalization of graphene withadatoms like hydrogen to enhance the otherwise weak spin-orbit coupling in graphene

by the conversion of the sp2 to sp3 hybridization of the graphene lattice Such hancement of the spin-orbit coupling is experimentally confirmed by demonstratingroom temperature spin Hall effect

en-Chapter 6: Similar to hydrogenation, the spin-orbit coupling in graphene can also beenhanced by introducing metallic adatoms like copper (Cu), gold (Au) or silver (Ag).

In this chapter, our present efforts towards the enhancement of graphene’s spin-orbitstrength by metal decoration will be discussed

Chapter 7: The conclusion and future perspectives of the work presented in this thesiswill be discussed

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2.2 Spin transport: Basic theory

In metals and semiconductors the electrons undergo scattering due to the presence

of disorder, impurities or phonons The resultant motion of electrons is equivalent

to a random walk problem in one dimensions [4] The relation between the resultantaverage velocity of the electrons to the applied electric field and system parameterslike the mean free path and average scattering time (momentum relaxation time) isobtained in the standard Drude formalism [6] Here, our aim is to review a similartheoretical formalism for the spins within the diffusive transport framework [4] For

this, consider a system with an electron density n such that n ↑ is the density of

spin-up electrons and n ↓ is the density of spin-down electrons, then

n = n ↑ + n ↓ (2.2.1)

while the spin density s is given by

s = n ↑ − n ↓ (2.2.2)

In the diffusive regime the spin-up and spin-down electrons can also be considered to

be performing random walks due to collisions In such scattering process the spins

are allowed to flip (spin-up to spin-down or vice-a-versa) and if f is the probability that a spin flips in the time τ , then the spin flip rate is f/τ Now to understand the

time evolution of the density of the spin states, let us assume that at time t and at

position x, the density of spin-up electrons n ↑ (x, t) is given by the densities at x-l and

x+l in the time interval t-τ If p+ and p − are the probabilities for the spin-flip process

at x-l and x+l, the spin-up density around (x,t) is

The actual spin flip probability within the time limit τ is of the order of 10 −6 , i.e.,

f <<1 Also p++p − =1 and p+-p − =∆p Substituting these conditions into equation (2.2.4) gives the relation for the spin-up density at (x,t) as

Figure 2.1: Decay of the spin density s as a function of the position x Here at x = 0 the spin density is normalized to 1 and as the distance increases from x = 0 the spins start to decay with a characteristic length scale λ s

where D = 12l τ2 is the diffusion coefficient, v d=τ l =µE is the drift velocity of electrons

in applied electric field E, µ is the mobility of the charge carriers, and τ1

s = 2f τ is thespin relaxation/dephasing length Since our focus is on the diffusion of spins in amedium, the spin drift-diffusion equation (2.2.8) can be solved by neglecting the driftterm

2.2.1 Spin diffusion without drift

The spin diffusion equation (2.2.8) neglecting the drift term is given by

where λ s is the spin relaxation length defined as √

Dτ s, and clearly shows that the

spin density decays exponentially with x with the characteristic length scale λ s The

length scale λ s tells us how far an electron spin can travel in the medium before itsinitial spin direction gets randomized

2.3.1 Electrical spin injection into a non-magnetic material

By the electrical spin injection we mean the creation of non-equilibrium population

of up and down spins in the material This can be achieved by the introduction

of a ferromagnetic material as the source of the spins, since in a ferromagnet due toexchange splitting [7,8], the density of states as well as the Fermi velocity for the spin-

up and spin-down sub-bands become different This results in different conductivitiesfor the spin-up and spin-down electrons and hence in the generation of spin polarized

current j ↑,↓, [9–15]

j ↑,↓ = σ ↑,↓ ∂µ ↑,↓

where σ ↑,↓ = e2N ↑,↓ D ↑,↓ is the spin up and spin down conductivity, e is the electric

charge, N↑,↓ is the spin dependent density of states at the Fermi energy and D↑,↓ =

1

3v F ↑,↓ l e ↑,↓ is the spin dependent diffusion coefficient with Fermi velocity v F ↑,↓ and

electron mean free path l e ↑,↓ for spin-up and spin down electrons and µ ↑,↓ is theelectrochemical potential of the spin species defined as

µ = µ ch − eV (2.3.2)

Here, µ ch is the chemical potential which by definition is the energy needed to addone electron to the system and accounts for the kinetic energy of the electrons, and

eV is the potential energy the electrons experience due to an electric field E Since

the spin-up and spin down current and conductivities are different, the bulk spinpolarization in the ferromagnet can be defined as

P = σ ↑ − σ ↓

σ ↑ + σ ↓ =

j ↑ − j ↓

j ↑ + j ↓ (2.3.3)where j ↑ − j ↓ = j s is the spin current, j ↑ + j ↓ = j is the total charge current and

σ ↑ + σ ↓ = σ is the total conductivity The relation for the spin current equation

(2.3.1) can now be rewritten as

From the above relations, it is clear that the variation in the electrochemical potential

of the up and down spins would result in the generation of a spin polarized currentand this can be achieved either by varying the density of spin polarized electrons(∇n) or by the application of an electric field E=-∇V.

2.3.2 Detection of the decaying spins

As discussed, in a diffusive material, the injected spin decay exponentially with a

characteristic length scale given by the spin relaxation length λ s and time scale given

by the spin relaxation time τ s The first electrical detection scheme based on charge coupling was proposed by Johnson and Silsbee [16] In a spin-charge coupling

spin-a non-mspin-agnetic mspin-aterispin-al with non-equilibrium spin populspin-ation when in contspin-act with spin-aferromagnet produces electrical current, thus allowing the electrical detection of spins

A second method is to use optical methods where spin polarized electrons recombinewith the unpolarized holes to emit circularly polarized light The spins can also bedetected by using the spin-valve effect [17] In the spin-valve effect, the injected spinsfrom the ferromagnet electrode into the non-magnetic material can be detected byusing a second ferromagnet Here, the relative orientation of magnetization of theinjector and detector ferromagnetic electrodes is important for the reliable detection